Download Algebra 2 Honors

Course Outlines
Name of the course:
Algebra 2 Honors
Course description:
In this course there is equal emphasis on theory and application with stress on
computation accuracy and problem solving.
Topics covered are properties of a number field, operations on numbers and
polynomials, linear, quadratic and cubic relations and functions, systems of
equations and inequalities, use of matrices and determinants, radicals, complex
numbers, conic sections, and polynomial and rational functions.
Essential Questions:
• When and why should we estimate?
• Is there a pattern?
• How does what we measure influence how we measure?
• How does how we measure influence what we measure or don’t
measure?
• What do good problem solvers do especially when they get
stuck?
• How precise should this solution be?
• What are the limits of this mathematical model and of
mathematical modeling in general?
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Topics:
Solving Linear Equations
Solving Absolute Value Equations
Solving Inequalities
Solving Compound and Absolute Value Inequalities
Linear Relations and Functions
Slope and Rate of Change
Writing Linear Equations
Absolute Value Functions
Graphing Linear and Absolute Value Inequalities
Solving Systems of Equations by Graphing
Solving Systems of Equations using Substitution
Solving Systems of Equations using Elimination
Solving Systems of Equations in Three Variables
Optimization with Linear Programming
Operations with Matrices
Cramer’s Rule
Solving Systems using Inverse Matrices
Graphing Quadratic Functions
Solving Quadratics by Graphing
Solving Quadratics by Factoring
Complex Numbers
Completing the Square
The Quadratic Formula and the Discriminant
Transformations of Quadratic Graphs
Quadratic Inequalities
Operations with Polynomials
Dividing Polynomials
Analyzing Graphs of Polynomials
Solving Polynomial Equations
The Remainder and Factor Theorems
Roots and Zeroes of Functions
Rational Zero Theorem
Nth roots
Operations with Radical Expressions
Rational Exponents
Solving Radical Equations and Inequalities
Rational Expressions and Equations
Conic Sections
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Assessment:
Homework
Quizzes
Tests
Solving Systems of Equations Common Assessment
Solving Systems of Inequalities and Linear Programming Common Assessment
Factoring and Solving Polynomials by Factoring Common Assessment
Laws of Exponents Common Assessment
Dividing Polynomials Common Assessment
Operations with Matrices Common Assessment
Quadratic Relations Common Assessment
Learning Standards
A.APR.6
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form
q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree
of r(x) less than the degree of b(x), using inspection, long division, or, for the
more complicated examples, a computer algebra system.
A.CED.1
Create equations and inequalities in one variable and use them to solve
problems. Include equations arising from linear and quadratic functions, and
simple rational and exponential functions.
A.CED.3
Represent constraints by equations or inequalities, and by systems of equations
and/or inequalities, and interpret solutions as viable or nonviable options in a
modeling context.
A.REI.2
Solve simple rational and radical equations in one variable, and give examples
showing how extraneous solutions may arise.
A.REI.5
Prove that, given a system of two equations in two variables, replacing one
equation by the sum of that equation and a multiple of the other produces a
system with the same solutions.
A.REI.6
Solve systems of linear equations exactly and approximately (e.g., with graphs),
focusing on pairs of linear equations in two variables.
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A.REI.12
Graph the solutions to a linear inequality in two variables as a half plane
(excluding the boundary in the case of a strict inequality), and graph the solution
set to a system of linear inequalities in two variables as the intersection of the
corresponding half-planes.
N.VM.7
(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the
payoffs in a game are doubled.
N.VM.8
Add, subtract, and multiply matrices of appropriate dimensions.
N.VM.9
Understand that, unlike multiplication of numbers, matrix multiplication for
square matrices is not a commutative operation, but still satisfies the associative
and distributive properties.
A.SSE.2
Use the structure of an expression to identify ways to rewrite it.
A.SSE.3
Choose and produce an equivalent form of an expression to reveal and explain
properties of the quantity represented by the expression. ★
a. Factor a quadratic expression to reveal the zeros of the function it
defines.
F.IF.4
For a function that models a relationship between two quantities, interpret key
features of graphs and tables in terms of the quantities, and sketch graphs
showing key features given a verbal description of the relationship. Key features
include: intercepts; intervals where the function is increasing, decreasing,
positive, or negative; relative maximums and minimums; symmetries; end
behavior; and periodicity.
F.IF.8
Write a function defined by an expression in different but equivalent forms to
reveal and explain different properties of the function.
a.
Use the process of factoring and completing the square in a quadratic
function to show zeros, extreme values, and symmetry of the graph, and interpret
these in terms of a context.
b.
Use the properties of exponents to interpret expressions for exponential
functions.
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N.RN.2
Rewrite expressions involving radicals and rational exponents using the
properties of exponents.
N.CN.1
Know there is a complex number I such that i2 = -1, and every complex number
has the form a + bi with a and b real
N.CN.2
Use the relation i2 = –1 and the commutative, associative, and distributive
properties to add, subtract, and multiply complex numbers.
Resources:
Glencoe Algebra 2 textbook
Teaching supplement to Glencoe Algebra 2
Teacher notes / assessments
Graphing Calculator
Kennebunk High School